The technology for determining and using the location of mobile devices has become widespread. Techniques employed use satellite (e.g., GPS) or terrestrial multilateration, or proximity detection (e.g., by knowledge of nearby cell towers or Wi-Fi hotspots). The result is a great convenience for users. With the proliferation of location-capable user equipment, applications have arisen that rely on the determination of whether a user's location is inside or outside a defined area, i.e., containment. An example is an application that tracks a delivery or service vehicle and generates an alert when it is within a certain radius of its destination point.
A location determination service, such as one used to estimate the location of mobile devices within a cellular telephone network, may generate a location estimate of a user (e.g., latitude and longitude), with a specified input confidence level and associated uncertainty. The input confidence level is a probability estimated, by the location system, that the actual device location is within the associated uncertainty area. Different location determination technologies may use different confidence levels, as well as different uncertainty shapes, with the most common uncertainty shape being a circle around the obtained location. The radius of such an uncertainty circle, or the semi-major axis of an uncertainty ellipse, is commonly referred to as the uncertainty value. A user of the location data may desire knowledge, with a specific probability, or likelihood, that the mobile device is inside or outside a defined geographic boundary.
Frequently, the need to assess whether a mobile device is inside or outside a defined geographic boundary is required in real-time. Also, a multitude of devices may need to be monitored simultaneously against a multitude of geographic boundaries. The requirement to assess a large number of devices against many boundaries can be computationally intensive. Being able to provide results of such assessments with as little delay as possible further adds computational demands on processers doing the assessment. This can place large and impractical memory, processing power and input/output demands on the associated processing systems. Minimizing the computational intensity of such assessments helps to reduce latency, increase processing capacity and minimize processing systems required. In other words, in conventional systems, the containment decision is often made in a processing-intensive manner by calculating the probability that the actual location lies on one side of the boundary, given the location estimate in combination with other factors, such as the uncertainty, the associated confidence level, and knowledge of the statistical performance of the location determination technology.